@misc{HeuerWernhard:2024:synthesis, author = {Jan Heuer and Christoph Wernhard}, title = {Synthesizing Strongly Equivalent Logic Programs: Beth Definability for Answer Set Programs via Craig Interpolation in First-Order Logic}, year = {2024}, publisher = {arXiv}, note = {Preprint: \url{http://arxiv.org/abs/2402.07696}}, abstract = {We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs $P$ and $Q$ and vocabulary $V$ (set of predicates) the existence of a program $R$ in $V$ such that $P \cup R$ and $P \cup Q$ are strongly equivalent can be expressed as a first-order entailment. Moreover, our result is effective: A program $R$ can be constructed from a Craig interpolant for this entailment, using a known first-order encoding for testing strong equivalence, which we apply in reverse to extract programs from formulas. As a further perspective, this allows transforming logic programs via transforming their first-order encodings. In a prototypical implementation, the Craig interpolation is performed by first-order provers based on clausal tableaux or resolution calculi. Our work shows how definability and interpolation, which underlie modern logic-based approaches to advanced tasks in knowledge representation, transfer to answer set programming.} }

@inproceedings{Wernhard:2024:sgcd, author = {Christoph Wernhard}, title = {Structure-Generating First-Order Theorem Proving}, year = {2024}, booktitle = {AReCCa 2023 -- Automated Reasoning with Connection Calculi, International Workshop}, editor = {Jens Otten and Wolfgang Bibel}, series = {CEUR Workshop Proceedings}, publisher = {CEUR-WS.org}, volume = {3613}, pages = {64--83}, url = {https://ceur-ws.org/Vol-3613/AReCCa2023_paper5.pdf}, note = {[ \href{http://cs.christophwernhard.com/papers/sgcd_handout.pdf}{Presentation slides} ]}, abstract = {Provers based on the connection method can become much more powerful than currently believed. We substantiate this thesis with certain generalizations of known techniques. In particular, we generalize proof structure enumeration interwoven with unification -- the proceeding of goal-driven connection and clausal tableaux provers -- to an interplay of goal- and axiom-driven processing. It permits lemma re-use and heuristic restrictions known from saturating provers. Proof structure terms, proof objects that allow to specify and implement various ways of building proofs, are central for our approach. Meredith's condensed detachment represents the prototypical base case of such proof structure terms. Hence, we focus on condensed detachment problems, first-order Horn problems of a specific form. Experiments show that for this problem class the approach keeps up with state-of-the-art first-order provers, leads to remarkably short proofs, solves an ATP challenge problem, and is useful in machine learning for ATP. A general aim is to make ATP more accessible to systematic investigations in the space between calculi and implementation aspects.} }

@inproceedings{wernhard:range:2023, author = {Christoph Wernhard}, title = {Range-Restricted and Horn Interpolation through Clausal Tableaux}, year = {2023}, booktitle = {Automated Reasoning with Analytic Tableaux and Related Methods: 32nd International Conference, TABLEAUX 2023}, publisher = {Springer}, series = {LNCS (LNAI)}, pages = {3--23}, volume = {14278}, doi = {10.1007/978-3-031-43513-3_1}, editor = {Revantha Ramanayake and Josef Urban}, note = {[ Preprint (extended version): \url{https://arxiv.org/abs/2306.03572} | \href{http://cs.christophwernhard.com/papers/range_handout.pdf}{Presentation slides} ]}, abstract = {We show how variations of range-restriction and also the Horn property can be passed from inputs to outputs of Craig interpolation in first-order logic. The proof system is clausal tableaux, which stems from first-order ATP. Our results are induced by a restriction of the clausal tableau structure, which can be achieved in general by a proof transformation, also if the source proof is by resolution/paramodulation. Primarily addressed applications are query synthesis and reformulation with interpolation. Our methodical approach combines operations on proof structures with the immediate perspective of feasible implementation through incorporating highly optimized first-order provers.} }

@inproceedings{mrcwzzwb:lemmas:2023, author = {Michael Rawson and Christoph Wernhard and Zsolt Zombori and Wolfgang Bibel}, title = {Lemmas: Generation, Selection, Application}, year = {2023}, booktitle = {Automated Reasoning with Analytic Tableaux and Related Methods: 32nd International Conference, TABLEAUX 2023}, publisher = {Springer}, series = {LNCS (LNAI)}, pages = {153--174}, volume = {14278}, doi = {10.1007/978-3-031-43513-3_9}, editor = {Revantha Ramanayake and Josef Urban}, note = {[ Preprint (extended version): \url{https://arxiv.org/abs/2303.05854} | \href{http://cs.christophwernhard.com/papers/lemmas_handout.pdf}{Presentation slides} ]}, abstract = {Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates useful lemmas for automated theorem provers, demonstrating improvement for several representative systems and solving a hard problem not solved by any system for twenty years. By focusing on condensed detachment problems we simplify the setting considerably, allowing us to get at the essence of lemmas and their role in proof search.} }

@inproceedings{RWZ:2023:aitp, author = {Michael Rawson and Christoph Wernhard and Zsolt Zombori}, title = {Learning to Identify Useful Lemmas from Failure}, year = {2023}, booktitle = {8th Conference on Artificial Intelligence and Theorem Proving, AITP 2023 (Informal Book of Abstracts)}, editor = {Michael R. Douglas and Thomas C. Hales and Cezary Kaliszyk and Stephan Schulz and Josef Urban}, note = {[ \href{http://aitp-conference.org/2023/abstract/AITP_2023_paper_18.pdf}{Extended abstract} | \href{http://aitp-conference.org/2023/slides/ZZ.pdf}{Presentation slides} ]} }

@article{bpw:journal:2023, author = {Michael Benedikt and C\'{e}cilia Pradic and Christoph Wernhard}, title = {Synthesizing Nested Relational Queries from Implicit Specifications: Via Model Theory and via Proof Theory}, year = {2023}, publisher = {arXiv}, note = {[ Preprint (submitted): \url{http://arxiv.org/abs/2212.03085} ]}, abstract = {Derived datasets can be defined implicitly or explicitly. An \emph{implicit definition} (of dataset $O$ in terms of datasets $\vec I$) is a logical specification involving two distinguished sets of relational symbols. One set of relations is for the ``source data'' $\vec I$, and the other is for the ``interface data'' $O$. Such a specification is a valid definition of $O$ in terms of $\vec I$, if any two models of the specification agreeing on $\vec I$ agree on $O$. In contrast, an \emph{explicit definition} is a transformation (or ``query'' below) that produces $O$ from $\vec I$. Variants of \emph{Beth's theorem} state that one can convert implicit definitions to explicit ones. Further, this conversion can be done effectively given a proof witnessing implicit definability in a suitable proof system. We prove the analogous implicit-to-explicit result for nested relations: implicit definitions, given in the natural logic for nested relations, can be converted to explicit definitions in the nested relational calculus (NRC). We first provide a model-theoretic argument for this result, which makes some additional connections that may be of independent interest between NRC queries, \emph{interpretations}, a standard mechanism for defining structure-to-structure translation in logic, and between interpretations and implicit to definability ``up to unique isomorphism''. The latter connection uses a variation of a result of Gaifman concerning ``relatively categorical'' theories. We also provide a proof-theoretic result that provides an effective argument: from a proof witnessing implicit definability, we can efficiently produce an NRC definition. This will involve introducing the appropriate proof system for reasoning with nested sets, along with some auxiliary Beth-type results for this system. As a consequence, we can effectively extract rewritings of NRC queries in terms of NRC views, given a proof witnessing that the query is determined by the views.} }

@article{wernhard:bibel:investigations:2023, author = {Christoph Wernhard and Wolfgang Bibel}, title = {Investigations into Proof Structures}, year = {2023}, publisher = {arXiv}, note = {[ Preprint (submitted): \url{https://arxiv.org/abs/2304.12827} ]}, abstract = {We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is applied in an exemplary manner to a coherent and comprehensive formal reconstruction and analysis of historical proofs of a widely-studied problem due to {\L}ukasiewicz. The underlying approach opens the door towards new systematic ways of generating lemmas in the course of proof search to the effects of reducing the search effort and finding shorter proofs. Among the numerous reported experiments along this line, a proof of {\L}ukasiewicz's problem was automatically discovered that is much shorter than any proof found before by man or machine.} }

@inproceedings{Benedikt:Pradic:Wernhard:2023:pods, author = {Michael Benedikt and C\'{e}cilia Pradic and Christoph Wernhard}, title = {Synthesizing Nested Relational Queries from Implicit Specifications}, year = {2023}, booktitle = {Principles of Database Systems, PODS 23}, doi = {10.1145/3584372.3588653}, pages = {33--45}, abstract = {Derived datasets can be defined implicitly or explicitly. An \emph{implicit definition} (of dataset $O$ in terms of datasets $\vec I$) is a logical specification involving the source data $\vec I$ and the interface data $O$. It is a valid definition of $O$ in terms of $\vec I$, if two models of the specification agreeing on $\vec I$ agree on $O$. In contrast, an \emph{explicit definition} is a query that produces $O$ from $\vec I$. Variants of \emph{Beth's theorem} state that one can convert implicit definitions to explicit ones. Further, this conversion can be done effectively given a proof witnessing implicit definability in a suitable proof system. We prove the analogous effective implicit-to-explicit result for nested relations: implicit definitions, given in the natural logic for nested relations, can be effectively converted to explicit definitions in the nested relational calculus (NRC). As a consequence, we can effectively extract rewritings of NRC queries in terms of NRC views, given a proof witnessing that the query is determined by the views.} }

@inproceedings{Wernhard:2022:aitp, author = {Christoph Wernhard}, title = {Compressed Combinatory Proof Structures and Blending Goal- with Axiom-Driven Reasoning: Perspectives for First-Order ATP with Condensed Detachment and Clausal Tableaux}, year = {2022}, booktitle = {7th Conference on Artificial Intelligence and Theorem Proving, AITP 2022 (Informal Book of Abstracts)}, editor = {Michael R. Douglas and Thomas C. Hales and Cezary Kaliszyk and Stephan Schulz and Josef Urban}, note = {[ \href{http://cs.christophwernhard.com/papers/aitp22-abstract.pdf}{Extended abstract} | \href{http://cs.christophwernhard.com/papers/aitp22-slides-handout-version.pdf}{Presentation slides} ]} }

@inproceedings{Wernhard:2022:ccs, author = {Christoph Wernhard}, title = {Generating Compressed Combinatory Proof Structures -- An Approach to Automated First-Order Theorem Proving}, year = {2022}, booktitle = {8th Workshop on Practical Aspects of Automated Reasoning, PAAR~2022}, series = {CEUR Workshop Proceedings}, publisher = {CEUR-WS.org}, volume = {3201}, editor = {Boris Konev and Claudia Schon and Alexander Steen}, note = {[ Preprint: \url{https://arxiv.org/abs/2209.12592} ]}, abstract = {Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these straightforwardly factor into shared subgraphs. To search for proofs, combinator terms can be enumerated, like clausal tableaux, interwoven with unification of formulas that are associated with nodes of the enumerated structures. To restrict the search space, the enumeration can be based on proof schemas defined as parameterized combinator terms. We introduce here this ``combinator term as proof structure'' approach to automated first-order proving, present an implementation and first experimental results. The approach builds on a term view of proof structures rooted in condensed detachment and the connection method. It realizes features known from the connection structure calculus, which has not been implemented so far.} }

@techreport{Wernhard:2022:cdtools, author = {Christoph Wernhard}, title = {{CD Tools} -- {C}ondensed Detachment and Structure Generating Theorem Proving (System Description)}, year = {2022}, doi = {10.48550/ARXIV.2207.08453}, publisher = {arXiv}, note = {\url{https://arxiv.org/abs/2207.08453}}, abstract = {CD Tools is a Prolog library for experimenting with condensed detachment in first-order ATP, which puts a recent formal view centered around proof structures into practice. From the viewpoint of first-order ATP, condensed detachment offers a setting that is relatively simple but with essential features and serious applications, making it attractive as a basis for developing and evaluating novel techniques. CD Tools includes specialized provers based on the enumeration of proof structures. We focus here on one of these, SGCD, which permits to blend goal- and axiom-driven proof search in particularly flexible ways. In purely goal-driven configurations it acts similarly to a prover of the clausal tableaux or connection method family. In blended configurations its performance is much stronger, close to state-of-the-art provers, while emitting relatively short proofs. Experiments show characteristics and application possibilities of the structure generating approach realized by that prover. For a historic problem often studied in ATP it produced a new proof that is much shorter than any known one.} }

@proceedings{soqe2021, title = {Proceedings of the Second Workshop on Second-Order Quantifier Elimination and Related Topics (SOQE 2021)}, year = {2021}, editor = {Renate A. Schmidt and Christoph Wernhard and Yizheng Zhao}, volume = {3009}, series = {CEUR Workshop Proceedings}, publisher = {CEUR-WS.org}, address = {Aachen}, issn = {1613-0073}, url = {http://ceur-ws.org/Vol-3009}, venue = {Online Event, associated with KR 2021, the 18th International Conference on Principles of Knowledge Representation and Reasoning}, eventdate = {2021-11-04} }

@inproceedings{Wernhard:2021:goedel:soqe, author = {Christoph Wernhard}, title = {Applying Second-Order Quantifier Elimination in Inspecting {G}{\"o}del's Ontological Proof}, booktitle = {Proceedings of the Second Workshop on Second-Order Elimination and Related Topics (SOQE 2021)}, editor = {Renate A. Schmidt and Christoph Wernhard and Yizheng Zhao}, year = {2021}, series = {CEUR Workshop Proceedings}, volume = {3009}, pages = {98--111}, url = {http://ceur-ws.org/Vol-3009/paper4.pdf}, note = {[ Preprint (extended version): \url{https://arxiv.org/abs/2110.11108} ]}, abstract = {In recent years, G{\"o}del's ontological proof and variations of it were formalized and analyzed with automated tools in various ways. We supplement these analyses with a modeling in an automated environment based on first-order logic extended by predicate quantification. Formula macros are used to structure complex formulas and tasks. The analysis is presented as a generated type-set document where informal explanations are interspersed with pretty-printed formulas and outputs of reasoners for first-order theorem proving and second-order quantifier elimination. Previously unnoticed or obscured aspects and details of G{\"o}del's proof become apparent. Practical application possibilities of second-order quantifier elimination are shown and the encountered elimination tasks may serve as benchmarks.} }

@inproceedings{WernhardBibel:2021:ProofStructures, author = {Christoph Wernhard and Wolfgang Bibel}, title = {Learning from {\L}ukasiewicz and {M}eredith: Investigations into Proof Structures}, booktitle = {Automated Deduction: \mbox{CADE 2021}}, editor = {Andr{\'e} Platzer and Geoff Sutcliffe}, year = {2021}, publisher = {Springer}, series = {LNCS (LNAI)}, pages = {58--75}, volume = {12699}, note = {[ Preprint (extended version): \url{https://arxiv.org/abs/2104.13645} | \href{http://cs.christophwernhard.com/papers/cade_2021_slides.pdf}{Presentation slides} ]}, doi = {10.1007/978-3-030-79876-5_4}, abstract = {The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the potential of guiding proof search in a more direct way. The studied problems are of the wide-spread form of ``axiom(s) and rule(s) imply goal(s)''. The features include the well-known concept of lemmas. For their elaboration both human and automated proofs of selected theorems are taken into a close comparative consideration. The study at the same time accounts for a coherent and comprehensive formal reconstruction of historical work by {\L}ukasiewicz, Meredith and others. First experiments resulting from the study indicate novel ways of lemma generation to supplement automated first-order provers of various families, strengthening in particular their ability to find short proofs.} }

@article{Wernhard:2021:Interpolation, author = {Christoph Wernhard}, title = {Craig Interpolation with Clausal First-Order Tableaux}, journal = {Journal of Automated Reasoning}, year = {2021}, pages = {647--690}, volume = {65}, number = {5}, doi = {10.1007/s10817-021-09590-3}, note = {[ Preprint: \url{ https://arxiv.org/abs/2008.03489} ]}, abstract = {We develop foundations for computing Craig-Lyndon interpolants of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient machine-oriented systems based on calculi of two families: goal-oriented such as model elimination and the connection method, and bottom-up such as the hypertableau calculus. We present the first interpolation method for first-order proofs represented by closed tableaux that proceeds in two stages, similar to known interpolation methods for resolution proofs. The first stage is an induction on the tableau structure, which is sufficient to compute propositional interpolants. We show that this can linearly simulate different prominent propositional interpolation methods that operate by an induction on a resolution deduction tree. In the second stage, interpolant lifting, quantified variables that replace certain terms (constants and compound terms) by variables are introduced. We justify the correctness of interpolant lifting (for the case without built-in equality) abstractly on the basis of Herbrand's theorem and for a different characterization of the formulas to be lifted than in the literature. In addition, we discuss various subtle aspects that are relevant for the investigation and practical realization of first-order interpolation based on clausal tableaux.} }

@inproceedings{Wernhard:2020:PIE, author = {Christoph Wernhard}, title = {Facets of the {PIE} Environment for Proving, Interpolating and Eliminating on the Basis of First-Order Logic}, booktitle = {Declarative Programming and Knowledge Management (DECLARE 2019), Revised Selected Papers}, editor = {Petra Hofstedt and Salvador Abreu and Ulrich John and Herbert Kuchen and Dietmar Seipel}, year = {2020}, series = {LNCS (LNAI)}, doi = {10.1007/978-3-030-46714-2_11}, volume = {12057}, pages = {160--177}, publisher = {Springer}, note = {[ Preprint: \url{https://arxiv.org/abs/2002.10892} ]}, abstract = {PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. Its main focus is on formulas, as constituents of complex formalizations that are structured through formula macros, and as outputs of reasoning tasks such as second-order quantifier elimination and Craig interpolation. It supports a workflow based on documents that intersperse macro definitions, invocations of reasoners, and LaTeX-formatted natural language text. Starting from various examples, the paper discusses features and application possibilities of PIE along with current limitations and issues for future research.} }

@inproceedings{Kittelmann:Wernhard:2020:KBSET, author = {Jana Kittelmann and Christoph Wernhard}, title = {{KBSET} -- Knowledge-Based Support for Scholarly Editing and Text Processing with Declarative {LaTeX} Markup and a Core Written in {SWI}-{P}rolog}, booktitle = {Declarative Programming and Knowledge Management (DECLARE 2019), Revised Selected Papers}, editor = {Petra Hofstedt and Salvador Abreu and Ulrich John and Herbert Kuchen and Dietmar Seipel}, year = {2020}, series = {LNCS (LNAI)}, publisher = {Springer}, pages = {178--196}, volume = {12057}, doi = {10.1007/978-3-030-46714-2_12}, note = {[ Preprint: \url{https://arxiv.org/abs/2002.10329} ]}, abstract = {KBSET is an environment that provides support for scholarly editing in two flavors: First, as a practical tool KBSET/Letters that accompanies the development of editions of correspondences (in particular from the 18th and 19th century), completely from source documents to PDF and HTML presentations. Second, as a prototypical tool KBSET/NER for experimentally investigating novel forms of working on editions that are centered around automated named entity recognition. KBSET can process declarative application-specific markup that is expressed in LaTeX notation and incorporate large external fact bases that are typically provided in RDF. KBSET includes specially developed LaTeX styles and a core system that is written in SWI-Prolog, which is used there in many roles, utilizing that it realizes the potential of Prolog as a unifying language.} }

@incollection{Kittelmann:Wernhard:halle:2019, author = {Jana Kittelmann and Christoph Wernhard}, title = {Von der Transkription zur Wissensbasis. Zum Zusammenspiel von digitalen Editionstechniken und Formen der Wissensrepr{\"a}sentation am Beispiel von Korrespondenzen Johann Georg Sulzers}, editor = {Jana Kittelmann and Anne Purschwitz}, booktitle = {Aufkl{\"a}rungsforschung digital. Konzepte, Methoden, Perspektiven}, series = {IZEA -- Kleine Schriften}, volume = {10/2019}, publisher = {Mitteldeutscher Verlag}, year = {2019}, pages = {84--114}, note = {[ Preprint: \url{http://www.sulzer-digital.de/papiere/transkription_wissensbasis.pdf} ]} }

@inproceedings{Wernhard:2019:PIE, author = {Christoph Wernhard}, title = {{PIE} -- {P}roving, Interpolating and Eliminating on the Basis of First-Order Logic}, booktitle = {Pre-proceedings of the DECLARE 2019 Conference}, editor = {Salvador Abreu and Petra Hofstedt and Ulrich John and Herbert Kuchen and Dietmar Seipel}, year = {2019}, series = {CoRR}, volume = {abs/1909.04870}, archiveprefix = {arXiv}, eprint = {1908.11137}, abstract = {PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and LaTeX-formatted natural language text. Invocation of various reasoners is supported: External provers as well as sub-systems of PIE, which include preprocessors, a Prolog-based first-order prover, methods for Craig interpolation and methods for second-order quantifier elimination.} }

@inproceedings{Kittelmann:Wernhard:2019:KBSET, author = {Jana Kittelmann and Christoph Wernhard}, title = {{KBSET} -- {K}nowledge-Based Support for Scholarly Editing and Text Processing}, booktitle = {Pre-proceedings of the DECLARE 2019 Conference}, editor = {Salvador Abreu and Petra Hofstedt and Ulrich John and Herbert Kuchen and Dietmar Seipel}, year = {2019}, series = {CoRR}, volume = {abs/1909.04870}, archiveprefix = {arXiv}, eprint = {1908.11135}, abstract = {KBSET supports a practical workflow for scholarly editing, based on using LaTeX with dedicated commands for semantics-oriented markup and a Prolog-implemented core system. Prolog plays there various roles: as query language and access mechanism for large Semantic Web fact bases, as data representation of structured documents and as a workflow model for advanced application tasks. The core system includes a LaTeX parser and a facility for the identification of named entities. We also sketch future perspectives of this approach to scholarly editing based on techniques of computational logic.} }

@techreport{Wernhard:2018:Interpolation, author = {Christoph Wernhard}, title = {Craig Interpolation and Access Interpolation with Clausal First-Order Tableaux}, institution = {Technische Universit{\"a}t Dresden}, number = {Knowledge Representation and Reasoning 18-01}, year = {2018}, journal = {ArXiv e-prints}, archiveprefix = {arXiv}, eprint = {1802.04982}, abstract = {We develop foundations for computing Craig interpolants and similar intermediates of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient machine-oriented systems based on calculi of two families: goal-oriented like model elimination and the connection method, and bottom-up like the hyper tableau calculus. The presented method for Craig-Lyndon interpolation involves a lifting step where terms are replaced by quantified variables, similar as known for resolution-based interpolation, but applied to a differently characterized ground formula and proven correct more abstractly on the basis of Herbrand's theorem, independently of a particular calculus. Access interpolation is a recent form of interpolation for database query reformulation that applies to first-order formulas with relativized quantifiers and constrains the quantification patterns of predicate occurrences. It has been previously investigated in the framework of Smullyan's non-clausal tableaux. Here, in essence, we simulate these with the more machine-oriented clausal tableaux through structural constraints that can be ensured either directly by bottom-up tableau construction methods or, for closed clausal tableaux constructed with arbitrary calculi, by postprocessing with restructuring transformations.} }

@proceedings{soqe2017, title = {Proceedings of the Workshop on Second-Order Quantifier Elimination and Related Topics, SOQE~2017}, year = {2017}, editor = {Patrick Koopmann and Sebastian Rudolph and Renate A. Schmidt and Christoph Wernhard}, volume = {2013}, series = {CEUR Workshop Proceedings}, publisher = {CEUR-WS.org}, issn = {1613-0073}, url = {http://ceur-ws.org/Vol-2013/}, venue = {Dresden, Germany}, eventdate = {2017-12-06/2017-12-08} }

@inproceedings{Wernhard:2017:Approximating, author = {Christoph Wernhard}, title = {Approximating Resultants of Existential Second-Order Quantifier Elimination upon Universal Relational First-Order Formulas}, booktitle = {Proceedings of the Workshop on Second-Order Quantifier Elimination and Related Topics, SOQE~2017}, editor = {Patrick Koopmann and Sebastian Rudolph and Renate A. Schmidt and Christoph Wernhard}, series = {CEUR Workshop Proceedings}, volume = {2013}, pages = {82--98}, publisher = {CEUR-WS.org}, year = {2017}, url = {http://ceur-ws.org/Vol-2013/paper17.pdf}, abstract = {We investigate second-order quantifier elimination for a class of formulas characterized by a restriction on the quantifier prefix: existential predicate quantifiers followed by universal individual quantifiers and a relational matrix. For a given second-order formula of this class a possibly infinite sequence of universal first-order formulas that have increasing strength and are all entailed by the second-order formula can be constructed. Any first-order consequence of the second-order formula is a consequence of some member of the sequence. The sequence provides a recursive base for the first-order theory of the second-order formula, in the sense investigated by Craig. The restricted formula class allows to derive further properties, for example that the set of those members of the sequence that are equivalent to the second-order formula, or, more generally, have the same first-order consequences, is co-recursively enumerable. Also the set of first-order formulas that entails the second-order formula is co-recursively enumerable. These properties are proven with formula-based tools used in automated deduction, such as domain closure axioms, eliminating individual quantifiers by ground expansion, predicate quantifier elimination with Ackermann's Lemma, Craig interpolation and decidability of the Bernays-Sch{\"o}nfinkel-Ramsey class} }

@techreport{Wernhard:2017:SolutionProblem:report, author = {Christoph Wernhard}, title = {The {B}oolean Solution Problem from the Perspective of Predicate Logic -- Extended Version}, institution = {Technische Universit{\"a}t Dresden}, journal = {ArXiv e-prints}, archiveprefix = {arXiv}, eprint = {1706.08329}, number = {Knowledge Representation and Reasoning 17-01}, year = {2017}, abstract = {Finding solution values for unknowns in Boolean equations was a principal reasoning mode in the \textit{Algebra of Logic} of the 19th century. Schr{\"o}der investigated it as \textit{Aufl{\"o}sungsproblem} (\textit{solution problem}). It is closely related to the modern notion of Boolean unification. Today it is commonly presented in an algebraic setting, but seems potentially useful also in knowledge representation based on predicate logic. We show that it can be modeled on the basis of first-order logic extended by second-order quantification. A wealth of classical results transfers, foundations for algorithms unfold, and connections with second-order quantifier elimination and Craig interpolation show up. Although for first-order inputs the set of solutions is recursively enumerable, the development of constructive methods remains a challenge. We identify some cases that allow constructions, most of them based on Craig interpolation, and show a method to take vocabulary restrictions on solution components into account.} }

@inproceedings{Wernhard:2017:SolutionProblem, author = {Christoph Wernhard}, title = {The {B}oolean Solution Problem from the Perspective of Predicate Logic}, booktitle = {11th International Symposium on Frontiers of Combining Systems, FroCoS 2017}, editor = {Clare Dixon and Marcelo Finger}, series = {LNCS (LNAI)}, volume = {10483}, pages = {333--350}, publisher = {Springer}, doi = {10.1007/978-3-319-66167-4_19}, year = {2017}, note = {[ \href{http://cs.christophwernhard.com/papers/solution.pdf}{Preprint} | \href{http://cs.christophwernhard.com/papers/frocos_2017_slides.pdf}{Presentation slides} ]}, abstract = {Finding solution values for unknowns in Boolean equations was a principal reasoning mode in the \textit{Algebra of Logic} of the 19th century. Schr{\"o}der investigated it as \textit{Aufl{\"o}sungsproblem} (\textit{solution problem}). It is closely related to the modern notion of Boolean unification. Today it is commonly presented in an algebraic setting, but seems potentially useful also in knowledge representation based on predicate logic. We show that it can be modeled on the basis of first-order logic extended by second-order quantification. A wealth of classical results transfers, foundations for algorithms unfold, and connections with second-order quantifier elimination and Craig interpolation show up.} }

@misc{Wernhard:2017:tableauxposter, author = {Christoph Wernhard}, title = {Craig Interpolation and Query Reformulation with Clausal First-Order Tableaux}, year = {2017}, note = {Poster presentation at Automated Reasoning with Analytic Tableaux and Related Methods: 26th International Conference, TABLEAUX 2017}, url = {http://cs.christophwernhard.com/papers/tableaux_2017_poster.pdf} }

@inproceedings{Wernhard:PAAR:2016, author = {Christoph Wernhard}, title = {The {PIE} system for Proving, Interpolating and Eliminating}, booktitle = {5th Workshop on Practical Aspects of Automated Reasoning, PAAR 2016}, editor = {Pascal Fontaine and Stephan Schulz and Josef Urban}, year = {2016}, abstract = {The PIE system aims at providing an environment for creating complex applications of automated first-order theorem proving techniques. It is embedded in Prolog. Beyond actual proving tasks, also interpolation and second-order quantifier elimination are supported. A macro feature and a \LaTeX\ formula pretty-printer facilitate the construction of elaborate formalizations from small, understandable and documented units. For use with interpolation and elimination, preprocessing operations allow to preserve the semantics of chosen predicates. The system comes with a built-in default prover that can compute interpolants.}, volume = {1635}, pages = {125--138}, url = {http://ceur-ws.org/Vol-1635/paper-11.pdf}, series = {CEUR Workshop Proceedings}, publisher = {CEUR-WS.org} }

@inproceedings{Kittelmann:Wernhard:AITP:2016, author = {Jana Kittelmann and Christoph Wernhard}, title = {Towards Knowledge-Based Assistance for Scholarly Editing}, booktitle = {1st Conference on Artificial Intelligence and Theorem Proving, {AITP} 2016 (Book of Abstracts)}, editor = {Thomas C. Hales and Cezary Kaliszyk and Stephan Schulz and Josef Urban}, year = {2016}, url = {http://aitp-conference.org/aitp_proceedings.pdf#page=29}, pages = {29--31}, note = {[ \href{http://cs.christophwernhard.com/kbset/papers/slides_aitp_2016.pdf}{Presentation slides} ]}, abstract = {We investigate possibilities to utilize techniques of computational logic for scholarly editing. Semantic Web technology already makes relevant large knowledge bases available in form of logic formulas. There are several further roles of logic-based reasoning in machine supported scholarly editing. KBSET, a free prototype system, provides a platform for experiments.} }

@inproceedings{Kittelmann:Wernhard:DHd:2016, author = {Jana Kittelmann and Christoph Wernhard}, title = {Knowledge-Based Support for Scholarly Editing and Text Processing}, booktitle = {DHd 2016 -- Digital Humanities im deutschsprachigen Raum: Modellierung -- Vernetzung -- Visualisierung. Die Digital Humanities als f{\"a}cher{\"u}bergreifendes Forschungsparadigma. Konferenzabstracts}, year = {2016}, doi = {10.5281/zenodo.4645317}, pages = {178--181}, publisher = {nisaba verlag}, address = {Duisburg}, note = {[ \href{http://cs.christophwernhard.com/kbset/papers/slides_dhd_2016.pdf}{Presentation slides (in German)} ]} }

@techreport{Wernhard:2015:behmann:report, author = {Christoph Wernhard}, title = {Heinrich {B}ehmann's Contributions to Second-Order Quantifier Elimination from the View of Computational Logic}, institution = {Technische Universit{\"a}t Dresden}, number = {Knowledge Representation and Reasoning 15-05}, year = {2015}, note = {Revised 2017}, journal = {ArXiv e-prints}, archiveprefix = {arXiv}, eprint = {1712.06868}, abstract = {For relational monadic formulas (the L{\"o}wenheim class) second-order quantifier elimination, which is closely related to computation of uniform interpolants, projection and forgetting - operations that currently receive much attention in knowledge processing - always succeeds. The decidability proof for this class by Heinrich Behmann from 1922 explicitly proceeds by elimination with equivalence preserving formula rewriting. Here we reconstruct the results from Behmann's publication in detail and discuss related issues that are relevant in the context of modern approaches to second-order quantifier elimination in computational logic. In addition, an extensive documentation of the letters and manuscripts in Behmann's bequest that concern second-order quantifier elimination is given, including a commented register and English abstracts of the German sources with focus on technical material. In the late 1920s Behmann attempted to develop an elimination-based decision method for formulas with predicates whose arity is larger than one. His manuscripts and the correspondence with Wilhelm Ackermann show technical aspects that are still of interest today and give insight into the genesis of Ackermann's landmark paper ``Untersuchungen {\"u}ber das Eliminationsproblem der mathematischen Logik'' from 1935, which laid the foundation of the two prevailing modern approaches to second-order quantifier elimination.} }

@misc{Wernhard:2015:Deduktionstreffen, author = {Christoph Wernhard}, title = {Some Fragments Towards Establishing Completeness Properties of Second-Order Quantifier Elimination Methods}, year = {2015}, note = {Poster presentation at Jahrestreffen der GI Fachgruppe Deduktionssysteme, associated with CADE-25}, url = {http://cs.christophwernhard.com/papers/poster_deduktionstreffen_2015.pdf} }

@inproceedings{Wernhard:2015:relmon, author = {Christoph Wernhard}, title = {Second-Order Quantifier Elimination on Relational Monadic Formulas -- {A} Basic Method and Some Less Expected Applications}, booktitle = {Automated Reasoning with Analytic Tableaux and Related Methods: 24th International Conference, TABLEAUX 2015}, year = {2015}, publisher = {Springer}, series = {LNCS (LNAI)}, volume = {9323}, pages = {249--265}, doi = {10.1007/978-3-319-24312-2_18}, editor = {Hans de Nivelle}, note = {[ \href{http://cs.christophwernhard.com/papers/tableaux_2015_slides.pdf}{Presentation slides} ]}, abstract = {For relational monadic formulas (the L{\"o}wenheim class) second-order quantifier elimination, which is closely related to computation of uniform interpolants, forgetting and projection, always succeeds. The decidability proof for this class by Behmann from 1922 explicitly proceeds by elimination with equivalence preserving formula rewriting. We reconstruct Behmann's method, relate it to the modern DLS elimination algorithm and show some applications where the essential monadicity becomes apparent only at second sight. In particular, deciding $\mathcal{ALCOQH}$ knowledge bases, elimination in DL-Lite knowledge bases, and the justification of the success of elimination methods for Sahlqvist formulas.} }

@techreport{Wernhard:2015:relmon:report, author = {Christoph Wernhard}, title = {Second-Order Quantifier Elimination on Relational Monadic Formulas -- {A} Basic Method and Some Less Expected Applications (Extended Version)}, institution = {Technische Universit{\"a}t Dresden}, url = {http://www.wv.inf.tu-dresden.de/Publications/2015/report-15-04.pdf}, number = {Knowledge Representation and Reasoning 15-04}, year = {2015}, abstract = {For relational monadic formulas (the L{\"o}wenheim class) second-order quantifier elimination, which is closely related to computation of uniform interpolants, forgetting and projection, always succeeds. The decidability proof for this class by Behmann from 1922 explicitly proceeds by elimination with equivalence preserving formula rewriting. We reconstruct Behmann's method, relate it to the modern DLS elimination algorithm and show some applications where the essential monadicity becomes apparent only at second sight. In particular, deciding $\mathcal{ALCOQH}$ knowledge bases, elimination in DL-Lite knowledge bases, and the justification of the success of elimination methods for Sahlqvist formulas.} }

@inproceedings{Wernhard:2014:DefinientiaARWDT, author = {Christoph Wernhard}, title = {Second-Order Characterizations of Definientia in Formula Classes}, editor = {Alexander Bolotov and Manfred Kerber}, booktitle = {Joint Automated Reasoning Workshop and Deduktionstreffen, ARW-DT 2014}, pages = {36--37}, year = {2014}, url = {http://www.cs.bham.ac.uk/~mmk/events/ARW-DT2014/proceedings.pdf}, note = {Workshop presentation [ \href{http://cs.christophwernhard.com/papers/arwdt2014.pdf}{Slides} ].} }

@inproceedings{Wernhard:2014:Patterns, author = {Christoph Wernhard}, title = {Application Patterns of Projection/Forgetting}, year = {2014}, booktitle = {\href{http://vsl2014.at/meetings/iPRA-index.html}{Workshop on Interpolation: From Proofs to Applications, iPRA 2014}}, editor = {Laura Kovacs and Georg Weissenbacher}, url = {http://cs.christophwernhard.com/papers/ipra14abstract.pdf}, note = {Workshop presentation [ \href{http://cs.christophwernhard.com/papers/ipra14.pdf} {Slides} ].} }

@techreport{Wernhard:2014:Definientia, author = {Christoph Wernhard}, title = {Second-Order Characterizations of Definientia in Formula Classes}, institution = {Technische Universit{\"a}t Dresden}, url = {http://www.wv.inf.tu-dresden.de/Publications/2014/report-2014-03.pdf}, number = {Knowledge Representation and Reasoning 14-03}, year = {2014}, abstract = {Predicate quantification can be applied to characterize definientia of a given formula that are in terms of a given set of predicates. Methods for second-order quantifier elimination and the closely related computation of forgetting, projection and uniform interpolants can then be applied to compute such definientia. Here we address the question, whether this principle can be transferred to definientia in given classes that allow efficient processing, such as Horn or Krom formulas. Indeed, if propositional logic is taken as basis, for the class of all formulas that are equivalent to a conjunction of atoms and the class of all formulas that are equivalent to a Krom formula, the existence of definientia as well as representative definientia themselves can be characterized in terms of predicate quantification. For the class of formulas that are equivalent to a Horn formula, this is possible with a special further operator. For first-order logic as basis, we indicate guidelines and open issues.} }

@inproceedings{KittelmannWernhard:2014:Pueckler, author = {Jana Kittelmann and Christoph Wernhard}, title = {{S}emantik, {L}inked {D}ata, {W}eb-{P}r{\"a}sentation: {G}rundlagen der {N}achlasserschlie{\ss}ung im {P}ortal www.pueckler-digital.de}, editor = {Anne Baillot and Anna Busch}, booktitle = {Workshop Datenmodellierung in digitalen Briefeditionen und ihre interpretatorische Leistung}, publisher = {Humboldt-Universit{\"a}t zu Berlin}, note = {Poster presentation, [ \href{http://cs.christophwernhard.com/papers/abstract_pueckler_digital.pdf}{Abstract} | \href{http://cs.christophwernhard.com/papers/poster_pueckler_digital.pdf}{Poster} ].}, year = {2014} }

@techreport{Wernhard:2014:VBQ, author = {Christoph Wernhard}, title = {Expressing View-Based Query Processing and Related Approaches with Second-Order Operators}, institution = {Technische Universit{\"a}t Dresden}, url = {http://www.wv.inf.tu-dresden.de/Publications/2014/report-2014-02.pdf}, number = {Knowledge Representation and Reasoning 14-02}, year = {2014} }

@inproceedings{Wernhard:2013:Toyelim, author = {Christoph Wernhard}, title = {Computing with Logic as Operator Elimination: The {ToyElim} System}, booktitle = {Applications of Declarative Programming and Knowledge Management, 19th International Conference (INAP 2011) and 25th Workshop on Logic Programming (WLP 2011), Revised Selected Papers}, editor = {Hans Tompits and Salvador Abreu and Johannes Oetsch and J{\"o}rg P{\"u}hrer and Dietmar Seipel and Masanobu Umeda and Armin Wolf}, series = {LNCS (LNAI)}, volume = {7773}, publisher = {Springer}, year = {2013}, pages = {289--296}, doi = {10.1007/978-3-642-41524-1_17}, note = {[ \href{http://cs.christophwernhard.com/papers/toyelim.pdf}{Preprint} ]}, abstract = {A prototype system is described whose core functionality is, based on propositional logic, the elimination of second-order operators, such as Boolean quantifiers and operators for projection, forgetting and circumscription. This approach allows to express many representational and computational tasks in knowledge representation -- for example computation of abductive explanations and models with respect to logic programming semantics -- in a uniform operational system, backed by a uniform classical semantic framework.} }

@article{DHW:2014:Suppression, title = {Modeling the Suppression Task under Weak Completion and Well-Founded Semantics}, author = {Emmanuelle-Anna Dietz and Steffen H{\"o}lldobler and Christoph Wernhard}, journal = {Journal of Applied Non-Classsical Logics}, volume = {24}, number = {1--2}, pages = {61--85}, year = {2014} }

@incollection{KittelmannWernhard:2013:Pueckler, author = {Jana Kittelmann and Christoph Wernhard}, title = {{S}emantik, {W}eb, {M}etadaten und digitale {E}dition: {G}rundlagen und {Z}iele der {E}rschlie{\ss}ung neuer {Q}uellen des {B}ranitzer {P}{\"u}ckler-{A}rchivs}, editor = {Irene Krebs and others}, booktitle = {Resonanzen. P{\"u}cklerforschung im Spannungsfeld zwischen Wissenschaft und Kunst. Ein Konferenzbericht.}, year = {2013}, publisher = {trafo Verlag}, address = {Berlin}, pages = {179--202} }

@inproceedings{KittelmannWernhard:2013:Nachlass, author = {Jana Kittelmann and Christoph Wernhard}, title = {{M}{\"o}glichkeiten der {R}epr{\"a}sentation von {N}achlassarchiven im {W}eb}, booktitle = {Fachtagung Semantische Technologien -- Verwertungsstrategien und Konvergenz, Humboldt-Universit{\"a}t zu Berlin, Position Papers}, year = {2013}, url = {http://semantic-media-web.de/referenten/?detail=57} }

@inproceedings{Wernhard:2013:Abduction, author = {Christoph Wernhard}, title = {Abduction in Logic Programming as Second-Order Quantifier Elimination}, booktitle = {9th International Symposium on Frontiers of Combining Systems, FroCoS 2013}, editor = {Pascal Fontaine and Christophe Ringeissen and Renate A. Schmidt}, series = {LNCS (LNAI)}, volume = {8152}, publisher = {Springer}, pages = {103--119}, year = {2013}, doi = {10.1007/978-3-642-40885-4_8}, abstract = {It is known that skeptical abductive explanations with respect to classical logic can be characterized semantically in a natural way as formulas with second-order quantifiers. Computing explanations is then just elimination of the second-order quantifiers. By using application patterns and generalizations of second-order quantification, like literal projection, the globally weakest sufficient condition and circumscription, we transfer these principles in a unifying framework to abduction with three non-classical semantics of logic programming: stable model, partial stable model and well-founded semantics. New insights are revealed about abduction with the partial stable model semantics.}, note = {[ \href{http://cs.christophwernhard.com/papers/abduction-lp-soqe.pdf}{Preprint (extended version)} ]} }

@inproceedings{MPW:2013:SAT, author = {Norbert Manthey and Tobias Philipp and Christoph Wernhard}, title = {Soundness of Inprocessing in Clause Sharing {SAT} Solvers}, booktitle = {Theory and Applications of Satisfiability Testing, 16th International Conference, SAT 2013}, editor = {Matti J{\"a}rvisalo and Allen Van Gelder}, series = {LNCS}, volume = {7962}, publisher = {Springer}, pages = {22--39}, year = {2013}, doi = {10.1007/978-3-642-39071-5_4}, note = {Received the SAT 2013 Best Paper Award [ \href{http://cs.christophwernhard.com/papers/inprocessing.pdf}{Preprint} ]}, abstract = {We present a formalism that models the computation of clause sharing portfolio solvers with inprocessing. The soundness of these solvers is not a straightforward property since shared clauses can make a formula unsatisfiable. Therefore, we develop characterizations of simplification techniques and suggest various settings how clause sharing and inprocessing can be combined. Our formalization models most of the recent implemented portfolio systems and we indicate possibilities to improve these. A particular improvement is a novel way to combine clause addition techniques -- like blocked clause addition -- with clause deletion techniques -- like blocked clause elimination or variable elimination.} }

@inproceedings{Wernhard:2012:HR, author = {Christoph Wernhard}, title = {Towards a Declarative Approach to Model Human Reasoning with Nonmonotonic Logics}, booktitle = {Human Reasoning and Automated Deduction: KI 2012 Workshop Proceedings}, pages = {41--48}, editor = {Thomas Barkowsky and Marco Ragni and Frieder Stolzenburg}, series = {Report Series of the Transregional Collaborative Research Center SFB/TR 8 Spatial Cognition}, volume = {SFB/TR 8 Report 032-09/2012}, year = {2012}, publisher = {Universit{\"a}t Bremen / Universit{\"a}t Freiburg, Germany}, note = {(\url{http://cs.christophwernhard.com/papers/hrad2012.pdf})}, abstract = {Stenning and van Lambalgen introduced an approach to model empirically studied human reasoning with nonmonotonic logics. Some of the research questions that have been brought up in this context concern the interplay of the open- and closed-world assumption, the suitability of particular logic programming semantics for the modeling of human reasoning, and the role of three-valued logic programming semantics and three-valued logics. We look into these questions from the view of a framework where logic programs that model human reasoning are represented declaratively and are mechanizable by classical formulas extended with certain second-order operators.} }

@article{Wernhard:2012:ProjCirc, author = {Christoph Wernhard}, title = {Projection and Scope-Determined Circumscription}, journal = {Journal of Symbolic Computation}, year = {2012}, volume = {47}, issue = {9}, pages = {1089--1108}, note = {[ \href{http://cs.christophwernhard.com/papers/projcirc.pdf}{Preprint} ]}, doi = {10.1016/j.jsc.2011.12.034}, abstract = {We develop a semantic framework that extends first-order logic by literal projection and a novel second semantically defined operator, ``raising'', which is only slightly different from literal projection and can be used to define a generalization of parallel circumscription with varied predicates in a straightforward and compact way. We call this variant of circumscription ``scope-determined'', since like literal projection and raising its effects are controlled by a so-called ``scope'', that is, a set of literals, as parameter. We work out formally a toolkit of propositions about projection, raising and circumscription and their interaction. It reveals some refinements of and new views on previously known properties. In particular, we apply it to show that well-foundedness with respect to circumscription can be expressed in terms of projection, and that a characterization of the consequences of circumscribed propositional formulas in terms of literal projection can be generalized to first-order logic and expressed compactly in terms of new variants of the strongest necessary and weakest sufficient condition.} }

@techreport{Wernhard:2011:HRLPCL, author = {Christoph Wernhard}, title = {Forward Human Reasoning Modeled by Logic Programming Modeled by Classical Logic with Circumscription and Projection}, institution = {Technische Universit{\"a}t Dresden}, year = {2011}, url = {http://www.wv.inf.tu-dresden.de/Publications/2011/report11-07.pdf}, number = {Knowledge Representation and Reasoning 11-07}, abstract = {Recently an approach to model human reasoning as studied in cognitive science by logic programming, has been introduced by Stenning and van Lambalgen and exemplified with the suppression task. We investigate this approach from the view of a framework where different logic programming semantics correspond to different translations of logic programs into formulas of classical two-valued logic extended by two second-order operators, circumscription and literal projection. Based on combining and extending previously known such renderings of logic programming semantics, we take semantics into account that have not yet been considered in the context of human reasoning, such as stable models and partial stable models. To model human reasoning, it is essential that only some predicates can be subjected to closed world reasoning, while others are handled by open world reasoning. In our framework, variants of familiar logic programing semantics that are extended with this feature are derived from a generic circumscription based representation. Further, we develop a two-valued representation of a three-valued logic that renders semantics considered for human reasoning based on the Fitting operator.} }

@inproceedings{Wernhard:2011:ToyElim, author = {Christoph Wernhard}, title = {Computing with Logic as Operator Elimination: The {ToyElim} System}, booktitle = {Proceedings of the 25th Workshop on Logic Programming, WLP 2011}, organization = {Technische Universit{\"a}t Wien}, series = {Infsys Research Report 1843-11-06}, pages = {94--98}, year = {2011}, journal = {ArXiv e-prints}, archiveprefix = {arXiv}, eprint = {1108.4891}, abstract = {A prototype system is described whose core functionality is, based on propositional logic, the elimination of second-order operators, such as Boolean quantifiers and operators for projection, forgetting and circumscription. This approach allows to express many representational and computational tasks in knowledge representation -- for example computation of abductive explanations and models with respect to logic programming semantics -- in a uniform operational system, backed by a uniform classical semantic framework.} }

@inproceedings{HPW:2011:AMHR, author = {Steffen H{\"o}lldobler and Tobias Philipp and Christoph Wernhard}, title = {An Abductive Model for Human Reasoning}, booktitle = {Logical Formalizations of Commonsense Reasoning, Papers from the AAAI 2011 Spring Symposium}, series = {AAAI Spring Symposium Series Technical Reports}, publisher = {AAAI Press}, year = {2011}, pages = {135--138}, note = {[ Preprint (extended version): \url{http://www.wv.inf.tu-dresden.de/Publications/2010/HoelldoblerPhilippWernhard.pdf} ]}, abstract = {In this paper we contribute to bridging the gap between human reasoning as studied in Cognitive Science and commonsense reasoning based on formal logics and formal theories. In particular, the suppression task studied in Cognitive Science provides an interesting challenge problem for human reasoning based on logic. The work presented in the paper is founded on the recent approach by Stenning and van Lambalgen to model human reasoning by means of logic programs with a specific three-valued completion semantics and a semantic fixpoint operator that yields a least model, as well as abduction. Their approach has been subsequently made more precise and technically accurate by switching to three-valued {\L}ukasiewicz logic. In this paper, we extend this refined approach by abduction. We show that the inclusion of abduction permits to adequately model additional empiric results reported from Cognitive Science. For the arising abductive reasoning tasks we give complexity results. Finally, we outline several open research issues that emerge from the application of logic to model human reasoning.} }

@inproceedings{Wernhard:2010:LP, author = {Christoph Wernhard}, title = {Circumscription and Projection as Primitives of Logic Programming}, booktitle = {Technical Communications of the 26th International Conference on Logic Programming, ICLP'10}, year = {2010}, volume = {7}, pages = {202--211}, editor = {M.~Hermenegildo and T.~Schaub}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, address = {Dagstuhl, Germany}, isbn = {978-3-939897-17-0}, issn = {1868-8969}, url = {http://drops.dagstuhl.de/opus/volltexte/2010/2598/}, doi = {10.4230/LIPIcs.ICLP.2010.281}, note = {[ \href{http://cs.christophwernhard.com/papers/logprog2010extended.pdf}{Preprint (extended version)} ]}, abstract = {We pursue a representation of logic programs as classical first-order sentences. Different semantics for logic programs can then be expressed by the way in which they are wrapped into - semantically defined - operators for circumscription and projection. (Projection is a generalization of second-order quantification.) We demonstrate this for the stable model semantics, Clark's completion and a three-valued semantics based on the Fitting operator. To represent the latter, we utilize the polarity sensitiveness of projection, in contrast to second-order quantification, and a variant of circumscription that allows to express predicate minimization in parallel with maximization. In accord with the aim of an integrated view on different logic-based representation techniques, the material is worked out on the basis of first-order logic with a Herbrand semantics.} }

@inproceedings{Wernhard:2009:ProjectionCircumscription, author = {Christoph Wernhard}, title = {Literal Projection and Circumscription}, booktitle = {Proceedings of the 7th International Workshop on First-Order Theorem Proving, FTP'09}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, volume = {556}, pages = {60--74}, year = {2010}, url = {http://ceur-ws.org/Vol-556}, editor = {Nicolas Peltier and Viorica Sofronie-Stokkermans}, note = {[ \href{http://cs.christophwernhard.com/papers/projection-circumscription.pdf}{Preprint (extended version)} ]}, abstract = {We develop a formal framework intended as a preliminary step for a single knowledge representation system that provides different representation techniques in a unified way. In particular we consider first-order logic extended by techniques for second-order quantifier elimination and non-monotonic reasoning. In this paper two independent results are developed. The background for the first result is literal projection, a generalization of second-order quantification which permits, so to speak, to quantify upon an arbitrary sets of ground literals, instead of just (all ground literals with) a given predicate symbol. We introduce an operator raise that is only slightly different from literal projection and can be used to define a generalization of predicate circumscription in a straightforward and compact way. We call this variant of circumscription scope-determined. Some properties of raise and scope-determined circumscription, also in combination with literal projection, are then shown. A previously known characterization of consequences of circumscribed formulas in terms of literal projection is generalized from propositional to first-order logic and proven on the basis of the introduced concepts. The second result developed in this paper is a characterization stable models in terms of circumscription. Unlike traditional characterizations, it does not recur onto syntactic notions like reduct and fixed-point construction. It essentially renders a recently proposed ``circumscription-like'' characterization in a compact way, without involvement of a non-classically interpreted connective.} }

@inproceedings{Wernhard:2009:Tableaux, title = {Tableaux for Projection Computation and Knowledge Compilation}, booktitle = {Automated Reasoning with Analytic Tableaux and Related Methods: 18th International Conference, TABLEAUX 2009}, editor = {Martin Giese and Arild Waaler}, pages = {325--340}, year = {2009}, author = {Christoph Wernhard}, publisher = {Springer}, series = {LNCS (LNAI)}, volume = {5607}, url = {http://cs.christophwernhard.com/papers/tableaux-projection.pdf}, doi = {10.1007/978-3-642-02716-1_24}, abstract = {Projection computation is a generalization of second-order quantifier elimination, which in turn is closely related to the computation of forgetting and of uniform interpolants. On the basis of a unified view on projection computation and knowledge compilation, we develop a framework for applying tableau methods to these tasks. It takes refinements from performance oriented systems into account. Formula simplifications are incorporated at the level of tableau structure modification, and at the level of simplifying encountered subformulas that are not yet fully compiled. In particular, such simplifications can involve projection computation, where this is possible with low cost. We represent tableau construction by means of rewrite rules on formulas, extended with some auxiliary functors, which is particularly convenient for formula transformation tasks. As instantiations of the framework, we discuss approaches to propositional knowledge compilation from the literature, including adaptions of DPLL, and the hyper tableau calculus for first-order clauses.} }

@book{Wernhard:2009:ProjectionElimination, author = {Christoph Wernhard}, title = {Automated Deduction for Projection Elimination}, number = {324}, series = {Dissertations in Artificial Intelligence}, publisher = {AKA Verlag/IOS Press}, address = {Heidelberg, Amsterdam}, year = {2009}, url = {http://www.iospress.nl/loadtop/load.php?isbn=9781586039837}, abstract = {Projection is a logic operation which allows to express tasks in knowledge representation. These tasks involve extraction or removal of knowledge concerning a given sub-vocabulary. It is a generalization of second-order quantification, permitting, so to speak, to `quantify' upon an arbitrary set of ground literals instead of just (all ground literals with) a given predicate symbol. In \textit{Automated Deduction for Projection Elimination}, a semantic characterization of projection for first-order logic is presented. On this basis, properties underlying applications and processing methods are derived. The computational processing of projection, called projection elimination in analogy to quantifier elimination, can be performed by adapted theorem proving methods. This is shown for resolvent generation and, more in depth, tableau construction. An abstract framework relates projection elimination with knowledge compilation and shows the adaption of key features of high performance tableau systems. As a prototypical instance, an adaption of a modern DPLL method, such as underlying state-of-the-art SAT solvers, is worked out. It generalizes various recent knowledge compilation methods and utilizes the interplay with projection elimination for efficiency improvements.} }

@inproceedings{Wernhard:2008:LiteralProjection, author = {Christoph Wernhard}, title = {Literal Projection for First-Order Logic}, booktitle = {Logics in Artificial Intelligence: 11th European Conference, JELIA 08}, editor = {Steffen H{\"o}lldobler and Carsten Lutz and Heinrich Wansing}, pages = {389--402}, publisher = {Springer}, series = {LNCS (LNAI)}, volume = {5293}, doi = {10.1007/978-3-540-87803-2_32}, year = {2008}, note = {[ \href{http://cs.christophwernhard.com/papers/literal-projection.pdf}{Preprint (extended version)} ]}, abstract = {The computation of literal projection generalizes predicate quantifier elimination by permitting, so to speak, quantifying upon an arbitrary sets of ground literals, instead of just (all ground literals with) a given predicate symbol. Literal projection allows, for example, to express predicate quantification upon a predicate just in positive or negative polarity. Occurrences of the predicate in literals with the complementary polarity are then considered as unquantified predicate symbols. We present a formalization of literal projection and related concepts, such as literal forgetting, for first-order logic with a Herbrand semantics, which makes these notions easy to access, since they are expressed there by means of straightforward relationships between sets of literals. With this formalization, we show properties of literal projection which hold for formulas that are free of certain links, pairs of literals with complementary instances, each in a different conjunct of a conjunction, both in the scope of a universal first-order quantifier, or one in a subformula and the other in its context formula. These properties can justify the application of methods that construct formulas without such links to the computation of literal projection. Some tableau methods and direct methods for second-order quantifier elimination can be understood in this way.} }

@inproceedings{PelzerWernhard:2007:EKrhyper, author = {Bj{\"o}rn Pelzer and Christoph Wernhard}, title = {System Description: \mbox{E-KRHyper}}, pages = {503--513}, booktitle = {Automated Deduction: \mbox{CADE-21}}, editor = {Frank Pfenning}, publisher = {Springer}, series = {LNCS (LNAI)}, volume = {4603}, url = {http://cs.christophwernhard.com/papers/ekrhyper.pdf}, doi = {10.1007/978-3-540-73595-3_37}, year = {2007}, abstract = {The E-KRHyper system is a model generator and theorem prover for first-order logic with equality. It implements the new E-hyper tableau calculus, which integrates a superposition-based handling of equality into the hyper tableau calculus. E-KRHyper extends our previous KRHyper system, which has been used in a number of applications in the field of knowledge representation. In contrast to most first order theorem provers, it supports features important for such applications, for example queries with predicate extensions as answers, handling of large sets of uniformly structured input facts, arithmetic evaluation and stratified negation as failure. It is our goal to extend the range of application possibilities of KRHyper by adding equality reasoning.} }

@techreport{Wernhard:2007:Tableaux, author = {Christoph Wernhard}, title = {{Tableaux Between Proving, Projection and Compilation}}, institution = {{Universit{\"a}t Koblenz-Landau}}, year = {2007}, number = {Arbeitsberichte aus dem Fachbereich Informatik 18/2007}, address = {Institut f{\"u}r Informatik, Universit{\"a}tsstr. 1, 56070 Koblenz, Germany}, abstract = {Generalized methods for automated theorem proving can be used to compute formula transformations such as projection elimination and knowledge compilation. We present a framework based on clausal tableaux suited for such tasks. These tableaux are characterized independently of particular construction methods, but important features of empirically successful methods are taken into account, especially dependency directed backjumping and branch local operation. As an instance of that framework an adaption of DPLL is described. We show that knowledge compilation methods can be essentially improved by weaving projection elimination partially into the compilation phase.} }

@inproceedings{Wernhard:2004:SKP, author = {Christoph Wernhard}, title = {Semantic Knowledge Partitioning}, booktitle = {Logics in Artificial Intelligence: 9th European Conference, JELIA 04}, editor = {Jos{\'e} J{\'u}lio Alferes and Jo{\~a}o Leite Leite}, year = {2004}, pages = {552--564}, publisher = {Springer}, series = {LNCS (LNAI)}, volume = {3229}, doi = {10.1007/978-3-540-30227-8_46}, url = {http://cs.christophwernhard.com/papers/skp-jelia.ps}, abstract = {Some operations to decompose a knowledge base (considered as a first order logic formula) in ways so that only its semantics determines the results are investigated. Intended uses include the extraction of ``parts'' relevant to an application, the exploration and utilizing of implicit possibilities of structuring a knowledge base and the formulation of query answers in terms of a signature demanded by an application. A semantic framework based on Herbrand interpretations is outlined. The notion of Ā“model relative to a scopeĀ” is introduced. It underlies the partitioning operations ``projection'' and ``forgetting'' and also provides a semantic account for certain formula simplification operations. An algorithmic approach which is based on resolution and may be regarded as a variation of the SCAN algorithm is discussed.} }

@inproceedings{Wernhard:2004:SKPShort, author = {Christoph Wernhard}, title = {Semantic Knowledge Partitioning (Extended Abstract)}, editor = {Ulrike Sattler}, booktitle = {Contributions to the Doctoral Programme of the Second International Joint Conference on Automated Reasoning, IJCAR 2004}, publisher = {CEUR-WS.org}, series = {CEUR Workshop Proceedings}, volume = {106}, year = {2004}, url = {http://ceur-ws.org/Vol-106/} }

@inproceedings{BaumgartnerEtAl:2003:KrhyperInside, author = {Peter Baumgartner and Ulrich Furbach and Margret Gross-Hardt and Thomas Kleemann and Christoph Wernhard}, title = {{KRH}yper {I}nside -- {M}odel Based Deduction in Applications}, booktitle = {Proceedings of the \mbox{CADE-19} workshop Challenges and Novel Applications for Automated Reasoning}, year = {2003}, pages = {55--72}, url = {http://cs.christophwernhard.com/papers/novel.ps}, url = {http://www.uclic.ucl.ac.uk/usr/jgow/cnaar.pdf}, abstract = {Three real world applications are depicted which all have a full first order theorem prover based on the hyper tableau calculus as their core component. These applications concern information retrieval in electronic publishing, the integration of description logics with other knowledge representation techniques and XML query processing.} }

@techreport{Wernhard:2003:KRHyper, author = {Christoph Wernhard}, title = {{System Description: {KRHyper}}}, institution = {{Universit{\"a}t Koblenz-Landau}}, year = {2003}, number = {Fachberichte Informatik 14--2003}, address = {Institut f{\"u}r Informatik, Universit{\"a}tsstr. 1, 56070 Koblenz, Germany}, note = {Presented at the \mbox{CADE-19} workshop \textit{Model Computation: Principles, Algorithms, Applications}.}, url = {http://cs.christophwernhard.com/papers/krhsys.ps}, abstract = {KRHyper is a first order logic theorem proving and model generation system based on the hyper tableau calculus. It is targeted for use as an embedded system within knowledge based applications. In contrast to most first order theorem provers, it supports features important for those applications, for example queries with predicate extensions as answers, handling of large sets of uniformly structured input facts, arithmetic evaluation and stratified negation as failure.} }

@unpublished{Wernhard:2002:InfraEngine, author = {Christoph Wernhard}, title = {{InfraEngine}: {I}nferencing in the {S}emantic {W}eb by Planning}, year = {2002}, note = {System description (edited 2007). (A prototype implementation can be downloaded from \url{http://www.infraengine.com/})}, url = {http://www.infraengine.com/papers/infra.pdf}, abstract = {The idea of InfraEngine is to help establishing a Semantic Web infrastructure by a specially adapted AI planning engine. Inputs are distributed Web documents in Semantic Web formats proposed by the World Wide Web Consortium. Outputs are also delivered in such formats. The user interface allows to browse Semantic Web data and to control the planning services from any Web browser. Also other programs can make use of these services. A small and understandable, but general, mechanism that can be used for different kinds of applications should be provided.} }

@unpublished{Wernhard:2001:SemWebProofs, author = {Christoph Wernhard}, title = {Representing Proofs in the {S}emantic {W}eb}, year = {2001}, note = {Working paper for Persist AG, Teltow, Germany}, url = {http://cs.christophwernhard.com/papers/papers/persist/swproofs.pdf}, abstract = {First steps towards an RDF format for exchanging proofs in the Semantic Web.} }

@unpublished{Wernhard:2000:SemWebApplications, author = {Christoph Wernhard}, title = {Two Short Term Applications of the {S}emantic {W}eb}, year = {2001}, note = {Working paper for Persist AG, Teltow, Germany}, url = {http://cs.christophwernhard.com/papers/persist/applic.pdf}, abstract = {We outline two application scenarios which might be in the realm of short term applications of the Semantic Web: a software packaging system and the organization of a business trip. Both of them can be solved with today's technology to some degree, so they do not show the novel potential of the Semantic Web in full. However considering Semantic Web solutions for them is useful to get a picture of the characteristics of the Semantic Web and become aware of some concrete technical issues.} }

@unpublished{Wernhard:2000:PlanningWeb, author = {Christoph Wernhard}, title = {The {P}lanning {W}eb in Action}, year = {2000}, note = {Working paper for Persist AG, Teltow, Germany}, url = {http://cs.christophwernhard.com/papers/persist/outline.pdf}, abstract = {We propose resource oriented inference as one way of bringing the Semantic Web into action. It provides a framework for expressing and processing a variety of tasks from areas such as planning, scheduling, manufacturing resource planning, product data management, configuration management, workflow management and simulation. Resource oriented inference as a part of the Semantic Web should allow such tasks to be performed within the scope of the World Wide Web. A prototypical application is be the purchase of a complex product with the help of the Web. The product consists of multiple parts, some of them complex products by themselves. Several services are required to compose the product. Subparts and services can be provided by different companies all over the world. Delivery time and cost of the product should be optimized.} }

@unpublished{Wernhard:2000:SemanticWebModeling, author = {Christoph Wernhard}, title = {Towards a {S}emantic {W}eb Modeling Language}, year = {2000}, note = {Working paper for Persist AG, Teltow, Germany. Presented at \textit{KnowTech 2000}, Leipzig}, url = {http://cs.christophwernhard.com/papers/persist/swmod.pdf}, abstract = {Outline of a small Web embedded language for specifying types and reasoning about them. Its main features are: (1.) From primitive types, that require from their instances just that they implement a single method, complex types can be constructed by a few operators, such as as a type intersection. This composition of type definitions maps to the composition of fragments of type definitions in different Web documents. (2.) Types are compared by structural equivalence and not based on their names. This facilitates combination of independently developed models and implicit association of types with given instances. (3.) The hyperlinking of expressions of the modeling language can be understood in terms of defining equations of a rewriting system. The left side of such a rewrite rule is an URI, the right side an expression. Hyperlink dereferencing corresponds to a rewrite step with such a rule.} }

@unpublished{Wernhard:1999:LBCP, author = {Christoph Wernhard}, title = {Experiments with a Linear Backward Chaining Planner}, url = {http://cs.christophwernhard.com/papers/exp.ps}, year = {1999}, note = {(Edited May 2003)}, abstract = {The performance of an implementation of the linear backward chaining planning algorithm is compared to other planning systems by means of the problem set of the first ai planning systems competition (AIPS-98).} }

@inproceedings{DahnEtAl:1998:MathlibMathematica, author = {Ingo Dahn and Andreas Haida and Thomas Honigmann and Christoph Wernhard}, title = {Using {M}athematica and Automated Theorem Provers to Access a Mathematical Library}, booktitle = {Proceedings of the \mbox{CADE-15} Workshop on Integration of Deductive Systems}, pages = {36--43}, note = {(Revised and extended version: \url{http://cs.christophwernhard.com/papers/integ.ps})}, url = {http://i12www.ira.uka.de/Workshop/notes.ps.gz}, year = {1998}, abstract = {We describe a concept for the cooperation of a computer algebra system, several automated theorem provers and a mathematical library. The purpose of this cooperation is to enable intelligent retrieval of theorems and definitions from the remote mathematical library. Automated theorem provers compete on remote machines to verify conjectures provided by the user in a local copy of Mathematica. They make use of a remote knowledge base which contains parts of the Mizar Mathematical Library.} }

@inproceedings{DahnWernhard:1997:Mathlib, author = {Ingo Dahn and Christoph Wernhard}, title = {First Order Proof Problems Extracted from an Article in the {Mizar} Mathematical Library}, booktitle = {International Workshop on First-Order Theorem Proving, FTP'97}, year = {1997}, series = {RISC-Linz Report Series No.\ 97--50}, pages = {58--62}, publisher = {Johannes Kepler Universit{\"a}t, Linz}, editor = {Maria Paola Bonacina and Ulrich Furbach}, url = {http://cs.christophwernhard.com/papers/ftp97.ps}, abstract = {Over the years, interactive theorem provers have built a large body of verified computer mathematics. The ILF Mathematical Library aims to make this knowledge available to other systems. One of the reasons for such a project is economy. Verification of software and hardware frequently requires the proof of purely mathematical theorems. It is obviously inefficient, to use the time of experts in the design of software or hardware systems to prove such theorems. Another reason for presenting a collection of mathematical theorems in a unified framework is safety. It should facilitate the verification of theorems in the library of one system by other systems. A third reason is dynamics of research. New interactive theorem provers should obtain the possibility to show their usability for real-world problems without having to reprove elementary mathematical facts. Last but not least, it is hoped that reproving theorems in a uniform mathematical library will be considered as a challenge to the development of automated theorem provers.} }

@mastersthesis{Wernhard:92:CLOSDB, author = {Christoph Wernhard}, title = {Entwurf und {I}mplementierung einer {D}atenbank\-schnitt\-stelle f{\"u}r das {C}ommon {L}isp {O}bject {S}ystem}, school = {Freie Universit{\"a}t Berlin}, address = {Berlin, Germany}, type = {Magisterarbeit}, year = {1992}, note = {(The system documentation is available from \url{http://cs.christophwernhard.com/closdb/}.)} }

@inproceedings{SchweppeEtAl:90:DBCLOS, author = {Heinz Schweppe and Christoph Wernhard and Jutta Estenfeld}, title = {{DB-CLOS}: {E}ine {D}atenbankschnittstelle f{\"u}r das {C}ommon {L}isp {O}bject {S}ystem}, booktitle = {K{\"u}nstliche Intelligenz in der Praxis}, year = {1990}, publisher = {Siemens AG}, editor = {W. Remmele} }

@inproceedings{Hydrasat:2009, author = {Christoph Baldow and Friedrich Gr{\"a}ter and Steffen H{\"o}lldobler and Norbert Manthey and Max Seelemann and Peter Steinke and Christoph Wernhard and Konrad Winkler and Erik Zenker}, title = {{HydraSAT} 2009.3 Solver Description}, booktitle = {SAT 2009 Competitive Event Booklet}, pages = {15--16}, editor = {Daniel Le Berre et al.}, url = {http://www.cril.univ-artois.fr/SAT09/solvers/booklet.pdf}, year = {2009} }